Average Error: 28.8 → 9.2
Time: 51.5s
Precision: binary64
Cost: 46280
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
↓
\[\begin{array}{l} t_1 := b + y \cdot \left(y + a\right)\\ t_2 := y \cdot t_1\\ t_3 := c + t_2\\ t_4 := y \cdot \left(z + y \cdot x\right)\\ t_5 := \left(\frac{z}{y} + x\right) - \left(x \cdot \frac{a}{y} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ t_6 := t_3 \cdot t_3\\ t_7 := t_1 \cdot t_1\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+70}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+48}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+130}:\\ \;\;\;\;\frac{t}{y \cdot t_3} + \left(i \cdot \left(\left(230661.510616 \cdot \frac{-1}{y \cdot t_6} + \left(\frac{1}{t_6} \cdot -27464.7644705 - \frac{t_4}{t_6}\right)\right) - \frac{t}{{y}^{2} \cdot t_6}\right) + \left(\frac{27464.7644705 + t_4}{t_1} + \left(230661.510616 \cdot \frac{1}{t_2} + c \cdot \left(\left(27464.7644705 \cdot \frac{-1}{t_2 \cdot t_1} + \left(230661.510616 \cdot \frac{-1}{t_1 \cdot \left({y}^{2} \cdot t_1\right)} - \frac{y \cdot x}{t_7}\right)\right) - \frac{z}{t_7}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]
(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
↓
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ b (* y (+ y a))))
        (t_2 (* y t_1))
        (t_3 (+ c t_2))
        (t_4 (* y (+ z (* y x))))
        (t_5 (- (+ (/ z y) x) (+ (* x (/ a y)) (* (/ b y) (/ x y)))))
        (t_6 (* t_3 t_3))
        (t_7 (* t_1 t_1)))
   (if (<= y -5.4e+70)
     t_5
     (if (<= y 1.16e+48)
       (/
        (fma (fma (fma (fma x y z) y 27464.7644705) y 230661.510616) y t)
        (fma (fma (fma (+ y a) y b) y c) y i))
       (if (<= y 3.9e+130)
         (+
          (/ t (* y t_3))
          (+
           (*
            i
            (-
             (+
              (* 230661.510616 (/ -1.0 (* y t_6)))
              (- (* (/ 1.0 t_6) -27464.7644705) (/ t_4 t_6)))
             (/ t (* (pow y 2.0) t_6))))
           (+
            (/ (+ 27464.7644705 t_4) t_1)
            (+
             (* 230661.510616 (/ 1.0 t_2))
             (*
              c
              (-
               (+
                (* 27464.7644705 (/ -1.0 (* t_2 t_1)))
                (-
                 (* 230661.510616 (/ -1.0 (* t_1 (* (pow y 2.0) t_1))))
                 (/ (* y x) t_7)))
               (/ z t_7)))))))
         t_5)))))
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b + (y * (y + a));
	double t_2 = y * t_1;
	double t_3 = c + t_2;
	double t_4 = y * (z + (y * x));
	double t_5 = ((z / y) + x) - ((x * (a / y)) + ((b / y) * (x / y)));
	double t_6 = t_3 * t_3;
	double t_7 = t_1 * t_1;
	double tmp;
	if (y <= -5.4e+70) {
		tmp = t_5;
	} else if (y <= 1.16e+48) {
		tmp = fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma((y + a), y, b), y, c), y, i);
	} else if (y <= 3.9e+130) {
		tmp = (t / (y * t_3)) + ((i * (((230661.510616 * (-1.0 / (y * t_6))) + (((1.0 / t_6) * -27464.7644705) - (t_4 / t_6))) - (t / (pow(y, 2.0) * t_6)))) + (((27464.7644705 + t_4) / t_1) + ((230661.510616 * (1.0 / t_2)) + (c * (((27464.7644705 * (-1.0 / (t_2 * t_1))) + ((230661.510616 * (-1.0 / (t_1 * (pow(y, 2.0) * t_1)))) - ((y * x) / t_7))) - (z / t_7))))));
	} else {
		tmp = t_5;
	}
	return tmp;
}

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end
↓
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b + Float64(y * Float64(y + a)))
	t_2 = Float64(y * t_1)
	t_3 = Float64(c + t_2)
	t_4 = Float64(y * Float64(z + Float64(y * x)))
	t_5 = Float64(Float64(Float64(z / y) + x) - Float64(Float64(x * Float64(a / y)) + Float64(Float64(b / y) * Float64(x / y))))
	t_6 = Float64(t_3 * t_3)
	t_7 = Float64(t_1 * t_1)
	tmp = 0.0
	if (y <= -5.4e+70)
		tmp = t_5;
	elseif (y <= 1.16e+48)
		tmp = Float64(fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma(Float64(y + a), y, b), y, c), y, i));
	elseif (y <= 3.9e+130)
		tmp = Float64(Float64(t / Float64(y * t_3)) + Float64(Float64(i * Float64(Float64(Float64(230661.510616 * Float64(-1.0 / Float64(y * t_6))) + Float64(Float64(Float64(1.0 / t_6) * -27464.7644705) - Float64(t_4 / t_6))) - Float64(t / Float64((y ^ 2.0) * t_6)))) + Float64(Float64(Float64(27464.7644705 + t_4) / t_1) + Float64(Float64(230661.510616 * Float64(1.0 / t_2)) + Float64(c * Float64(Float64(Float64(27464.7644705 * Float64(-1.0 / Float64(t_2 * t_1))) + Float64(Float64(230661.510616 * Float64(-1.0 / Float64(t_1 * Float64((y ^ 2.0) * t_1)))) - Float64(Float64(y * x) / t_7))) - Float64(z / t_7)))))));
	else
		tmp = t_5;
	end
	return tmp
end

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(c + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(z / y), $MachinePrecision] + x), $MachinePrecision] - N[(N[(x * N[(a / y), $MachinePrecision]), $MachinePrecision] + N[(N[(b / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$3 * t$95$3), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$1 * t$95$1), $MachinePrecision]}, If[LessEqual[y, -5.4e+70], t$95$5, If[LessEqual[y, 1.16e+48], N[(N[(N[(N[(N[(x * y + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(N[(y + a), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+130], N[(N[(t / N[(y * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(N[(230661.510616 * N[(-1.0 / N[(y * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(1.0 / t$95$6), $MachinePrecision] * -27464.7644705), $MachinePrecision] - N[(t$95$4 / t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t / N[(N[Power[y, 2.0], $MachinePrecision] * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(27464.7644705 + t$95$4), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(230661.510616 * N[(1.0 / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(N[(27464.7644705 * N[(-1.0 / N[(t$95$2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 * N[(-1.0 / N[(t$95$1 * N[(N[Power[y, 2.0], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * x), $MachinePrecision] / t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]

\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\begin{array}{l}
t_1 := b + y \cdot \left(y + a\right)\\
t_2 := y \cdot t_1\\
t_3 := c + t_2\\
t_4 := y \cdot \left(z + y \cdot x\right)\\
t_5 := \left(\frac{z}{y} + x\right) - \left(x \cdot \frac{a}{y} + \frac{b}{y} \cdot \frac{x}{y}\right)\\
t_6 := t_3 \cdot t_3\\
t_7 := t_1 \cdot t_1\\
\mathbf{if}\;y \leq -5.4 \cdot 10^{+70}:\\
\;\;\;\;t_5\\

\mathbf{elif}\;y \leq 1.16 \cdot 10^{+48}:\\
\;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\

\mathbf{elif}\;y \leq 3.9 \cdot 10^{+130}:\\
\;\;\;\;\frac{t}{y \cdot t_3} + \left(i \cdot \left(\left(230661.510616 \cdot \frac{-1}{y \cdot t_6} + \left(\frac{1}{t_6} \cdot -27464.7644705 - \frac{t_4}{t_6}\right)\right) - \frac{t}{{y}^{2} \cdot t_6}\right) + \left(\frac{27464.7644705 + t_4}{t_1} + \left(230661.510616 \cdot \frac{1}{t_2} + c \cdot \left(\left(27464.7644705 \cdot \frac{-1}{t_2 \cdot t_1} + \left(230661.510616 \cdot \frac{-1}{t_1 \cdot \left({y}^{2} \cdot t_1\right)} - \frac{y \cdot x}{t_7}\right)\right) - \frac{z}{t_7}\right)\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;t_5\\


\end{array}

Error

Derivation

  1. Split input into 3 regimes

  2. if y < -5.3999999999999999e70 or 3.9000000000000002e130 < y

    1. Initial program 63.6

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

    2. Simplified63.6

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}} \]
      Proof
      (/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 x y z) y 54929528941/2000000) y 28832688827/125000) y t) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x y) z)) y 54929528941/2000000) y 28832688827/125000) y t) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000)) y 28832688827/125000) y t) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000)) y t) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t)) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 y a) y) b)) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c)) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))): 1 points increase in error, 0 points decrease in error

    3. Applied egg-rr63.6

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}} \]

    4. Taylor expanded in y around inf 24.6

      \[\leadsto \color{blue}{\left(\frac{z}{y} + \left(27464.7644705 \cdot \frac{1}{{y}^{2}} + x\right)\right) - \left(\frac{\left(z - a \cdot x\right) \cdot a}{{y}^{2}} + \left(\frac{a \cdot x}{y} + \frac{b \cdot x}{{y}^{2}}\right)\right)} \]

    5. Simplified15.0

      \[\leadsto \color{blue}{\left(\left(\left(\frac{z}{y} + \frac{27464.7644705}{y \cdot y}\right) + x\right) - \frac{a}{y} \cdot \frac{z - a \cdot x}{y}\right) - \left(\frac{a}{y} \cdot x + \frac{b}{y} \cdot \frac{x}{y}\right)} \]
      Proof
      (-.f64 (-.f64 (+.f64 (+.f64 (/.f64 z y) (/.f64 54929528941/2000000 (*.f64 y y))) x) (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 a x)) y))) (+.f64 (*.f64 (/.f64 a y) x) (*.f64 (/.f64 b y) (/.f64 x y)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (+.f64 (/.f64 z y) (/.f64 (Rewrite<= metadata-eval (*.f64 54929528941/2000000 1)) (*.f64 y y))) x) (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 a x)) y))) (+.f64 (*.f64 (/.f64 a y) x) (*.f64 (/.f64 b y) (/.f64 x y)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (+.f64 (/.f64 z y) (/.f64 (*.f64 54929528941/2000000 1) (Rewrite<= unpow2_binary64 (pow.f64 y 2)))) x) (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 a x)) y))) (+.f64 (*.f64 (/.f64 a y) x) (*.f64 (/.f64 b y) (/.f64 x y)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (+.f64 (/.f64 z y) (Rewrite<= associate-*r/_binary64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))))) x) (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 a x)) y))) (+.f64 (*.f64 (/.f64 a y) x) (*.f64 (/.f64 b y) (/.f64 x y)))): 3 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (Rewrite<= associate-+r+_binary64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x))) (*.f64 (/.f64 a y) (/.f64 (-.f64 z (*.f64 a x)) y))) (+.f64 (*.f64 (/.f64 a y) x) (*.f64 (/.f64 b y) (/.f64 x y)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 a (-.f64 z (*.f64 a x))) (*.f64 y y)))) (+.f64 (*.f64 (/.f64 a y) x) (*.f64 (/.f64 b y) (/.f64 x y)))): 13 points increase in error, 3 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x)) (/.f64 (Rewrite=> *-commutative_binary64 (*.f64 (-.f64 z (*.f64 a x)) a)) (*.f64 y y))) (+.f64 (*.f64 (/.f64 a y) x) (*.f64 (/.f64 b y) (/.f64 x y)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x)) (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (Rewrite<= unpow2_binary64 (pow.f64 y 2)))) (+.f64 (*.f64 (/.f64 a y) x) (*.f64 (/.f64 b y) (/.f64 x y)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x)) (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2))) (+.f64 (Rewrite<= associate-/r/_binary64 (/.f64 a (/.f64 y x))) (*.f64 (/.f64 b y) (/.f64 x y)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x)) (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2))) (+.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 a x) y)) (*.f64 (/.f64 b y) (/.f64 x y)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x)) (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2))) (+.f64 (/.f64 (*.f64 a x) y) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 b x) (*.f64 y y))))): 14 points increase in error, 6 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x)) (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2))) (+.f64 (/.f64 (*.f64 a x) y) (/.f64 (*.f64 b x) (Rewrite<= unpow2_binary64 (pow.f64 y 2))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--r+_binary64 (-.f64 (+.f64 (/.f64 z y) (+.f64 (*.f64 54929528941/2000000 (/.f64 1 (pow.f64 y 2))) x)) (+.f64 (/.f64 (*.f64 (-.f64 z (*.f64 a x)) a) (pow.f64 y 2)) (+.f64 (/.f64 (*.f64 a x) y) (/.f64 (*.f64 b x) (pow.f64 y 2)))))): 0 points increase in error, 0 points decrease in error

    6. Taylor expanded in y around inf 12.0

      \[\leadsto \color{blue}{\left(\frac{z}{y} + x\right)} - \left(\frac{a}{y} \cdot x + \frac{b}{y} \cdot \frac{x}{y}\right) \]

    if -5.3999999999999999e70 < y < 1.15999999999999992e48

    1. Initial program 4.8

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

    2. Simplified4.8

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}} \]
      Proof
      (/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 x y z) y 54929528941/2000000) y 28832688827/125000) y t) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x y) z)) y 54929528941/2000000) y 28832688827/125000) y t) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000)) y 28832688827/125000) y t) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000)) y t) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t)) (fma.f64 (fma.f64 (fma.f64 (+.f64 y a) y b) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 y a) y) b)) y c) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c)) y i)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) 54929528941/2000000) y) 28832688827/125000) y) t) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))): 1 points increase in error, 0 points decrease in error

    if 1.15999999999999992e48 < y < 3.9000000000000002e130

    1. Initial program 58.1

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

    2. Taylor expanded in i around 0 51.3

      \[\leadsto \color{blue}{\frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{{y}^{2} \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \frac{230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)}{c + y \cdot \left(\left(y + a\right) \cdot y + b\right)}\right)} \]

    3. Taylor expanded in c around 0 33.0

      \[\leadsto \frac{t}{y \cdot \left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(-1 \cdot \left(i \cdot \left(\frac{t}{{y}^{2} \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)\right)} + \left(27464.7644705 \cdot \frac{1}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)} + \frac{\left(y \cdot x + z\right) \cdot y}{\left(c + y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot \left(c + \left(b + y \cdot \left(a + y\right)\right) \cdot y\right)}\right)\right)\right)\right) + \color{blue}{\left(\frac{27464.7644705 + \left(y \cdot x + z\right) \cdot y}{\left(y + a\right) \cdot y + b} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(\left(y + a\right) \cdot y + b\right)} + -1 \cdot \left(c \cdot \left(\frac{z}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(\left(y + a\right) \cdot y + b\right)} + \left(27464.7644705 \cdot \frac{1}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(y \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \left(230661.510616 \cdot \frac{1}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left({y}^{2} \cdot \left(\left(y + a\right) \cdot y + b\right)\right)} + \frac{y \cdot x}{\left(b + y \cdot \left(a + y\right)\right) \cdot \left(\left(y + a\right) \cdot y + b\right)}\right)\right)\right)\right)\right)\right)}\right) \]
  3. Recombined 3 regimes into one program.

  4. Final simplification9.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+70}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(x \cdot \frac{a}{y} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+48}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+130}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} + \left(i \cdot \left(\left(230661.510616 \cdot \frac{-1}{y \cdot \left(\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\right)} + \left(\frac{1}{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} \cdot -27464.7644705 - \frac{y \cdot \left(z + y \cdot x\right)}{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\right)\right) - \frac{t}{{y}^{2} \cdot \left(\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\right)}\right) + \left(\frac{27464.7644705 + y \cdot \left(z + y \cdot x\right)}{b + y \cdot \left(y + a\right)} + \left(230661.510616 \cdot \frac{1}{y \cdot \left(b + y \cdot \left(y + a\right)\right)} + c \cdot \left(\left(27464.7644705 \cdot \frac{-1}{\left(y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot \left(b + y \cdot \left(y + a\right)\right)} + \left(230661.510616 \cdot \frac{-1}{\left(b + y \cdot \left(y + a\right)\right) \cdot \left({y}^{2} \cdot \left(b + y \cdot \left(y + a\right)\right)\right)} - \frac{y \cdot x}{\left(b + y \cdot \left(y + a\right)\right) \cdot \left(b + y \cdot \left(y + a\right)\right)}\right)\right) - \frac{z}{\left(b + y \cdot \left(y + a\right)\right) \cdot \left(b + y \cdot \left(y + a\right)\right)}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(x \cdot \frac{a}{y} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error9.2
Cost29388
\[\begin{array}{l} t_1 := y \cdot \left(z + y \cdot x\right)\\ t_2 := 27464.7644705 + t_1\\ t_3 := \left(\frac{z}{y} + x\right) - \left(x \cdot \frac{a}{y} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ t_4 := b + y \cdot \left(y + a\right)\\ t_5 := y \cdot t_4\\ t_6 := c + t_5\\ t_7 := y \cdot t_6\\ t_8 := t_4 \cdot t_4\\ t_9 := t_6 \cdot t_6\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+70}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+46}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot t_2\right)}{i + t_7}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+130}:\\ \;\;\;\;\frac{t}{t_7} + \left(i \cdot \left(\left(230661.510616 \cdot \frac{-1}{y \cdot t_9} + \left(\frac{1}{t_9} \cdot -27464.7644705 - \frac{t_1}{t_9}\right)\right) - \frac{t}{{y}^{2} \cdot t_9}\right) + \left(\frac{t_2}{t_4} + \left(230661.510616 \cdot \frac{1}{t_5} + c \cdot \left(\left(27464.7644705 \cdot \frac{-1}{t_5 \cdot t_4} + \left(230661.510616 \cdot \frac{-1}{t_4 \cdot \left({y}^{2} \cdot t_4\right)} - \frac{y \cdot x}{t_8}\right)\right) - \frac{z}{t_8}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 2
Error9.5
Cost4292
\[\begin{array}{l} t_1 := \frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \left(x \cdot \frac{a}{y} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \end{array} \]
Alternative 3
Error11.9
Cost2380
\[\begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)\\ t_2 := \left(\frac{z}{y} + x\right) - \left(x \cdot \frac{a}{y} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -8.6 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-52}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 4
Error11.4
Cost2380
\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \left(x \cdot \frac{a}{y} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.85 \cdot 10^{-47}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+54}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + \left(y + a\right) \cdot \left(y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 5
Error11.7
Cost2120
\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \left(x \cdot \frac{a}{y} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+27}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 6
Error12.2
Cost1992
\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \left(x \cdot \frac{a}{y} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+27}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 7
Error14.8
Cost1872
\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \left(x \cdot \frac{a}{y} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -240:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 8
Error14.4
Cost1864
\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \left(x \cdot \frac{a}{y} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+27}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 9
Error13.6
Cost1864
\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \left(x \cdot \frac{a}{y} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 10
Error17.0
Cost1744
\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \left(x \cdot \frac{a}{y} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -44:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-67}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 11
Error17.4
Cost1744
\[\begin{array}{l} t_1 := \left(\frac{z}{y} + x\right) - \left(x \cdot \frac{a}{y} + \frac{b}{y} \cdot \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -240:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 25000000000:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 12
Error19.2
Cost1616
\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.114:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-68}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 13
Error18.2
Cost1616
\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -28:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-67}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + z \cdot \left(y \cdot y\right)\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 14
Error18.4
Cost1484
\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.232:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + a \cdot \left(y \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 15
Error26.6
Cost1236
\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ t_2 := t + y \cdot 230661.510616\\ t_3 := \frac{t_2}{i}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.0088:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-134}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-72}:\\ \;\;\;\;\frac{t_2}{y \cdot c}\\ \mathbf{elif}\;y \leq 0.082:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 16
Error19.4
Cost1100
\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.23:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 17
Error25.8
Cost972
\[\begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.05:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 18
Error32.1
Cost852
\[\begin{array}{l} t_1 := \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -46:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+105}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 19
Error29.5
Cost844
\[\begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -0.033:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-19}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 20
Error31.8
Cost456
\[\begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 530000000:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 21
Error47.0
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022329 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))